Stopband Constraints Research Articles

Designing radar transmit sequences satisfying simultaneous temporal integrated sidelobe level and spectral stopband constraints

Due to their nice properties, unimodular sequences possessing low autocorrelation sidelobes have already been employed as transmit waveforms in numerous radar systems. It could also be desired to have a transmit waveform which avoids certain frequency bands allocated for specific communication applications. Hence, adaptation and specific design of the waveform spectrum might also be essential. Accordingly, in this manuscript, we propose two alternative algorithms for designing radar transmit sequences satisfying simultaneous temporal integrated sidelobe level (ISL) and spectral stopband constraints. The proposed algorithms utilize the majorization-minimization (MM) method for directly minimizing ISL by first proposing a majorizing function in place of the objective function of the minimization problem. Then, solution of the minimization problem is obtained in an iterative manner. Accelerated versions of the newly proposed algorithms are also derived to facilitate their fast convergence. We also present numerical examples for comparing performances of our newly proposed methods against some existing methods from the literature in terms of computation time, number of iterations, and level of suppression in stopbands.

Designing Unimodular Waveform with Low Range Sidelobes and Stopband for Cognitive Radar via Relaxed Alternating Projection

Cognitive radar could adapt the spectrum of waveforms in response to information regarding the changing environment, so as to avoid narrowband interference or electronic jamming. Besides stopband constraints, low range sidelobes and unimodular property are also desired. In this paper, we propose a Spectral Approximation Relaxed Alternating Projection (SARAP) method, to synthesize unimodular waveform with low range sidelobes and spectral power suppressed. This novel method, based on phase retrieval and relaxed alternating projection, could convert the correlation optimization into the spectrum approximation via the Fast Fourier Transform (FFT). Moreover, by virtue of the relaxation factor and accelerated factor, SARAP can exploit local area and more likely converge to the global solution. Numerical trials have demonstrated that SARAP could achieve excellent performance and computational efficiency which will facilitate the real-time design.

Design of IIR Digital Differentiators Using Constrained Optimization

A new optimization method for the design of fullband and lowpass IIR digital differentiators is proposed. In the new method, the passband phase-response error is minimized under the constraint that the maximum passband amplitude-response relative error is below a prescribed level. For lowpass IIR differentiators, an additional constraint is introduced to limit the average squared amplitude response in the stopband so as to minimize any high-frequency noise that may be present. Extensive experimental results are included, which show that the differentiators designed using the proposed method have much smaller maximum phase-response error for the same passband amplitude-response error and stopband constraints when compared with several differentiators designed using state-of-the-art competing methods.

A Novel Approach to the Design of Oversampling Low-Delay Complex-Modulated Filter Bank Pairs

In this contribution we present a method to design prototype filters of oversampling uniform complex-modulated FIR filter bank pairs. Especially, we present a noniterative two-step procedure: (i) design of analysis prototype filter with minimum group delay and approximately linear-phase frequency response in the passband and the transition band and (ii) Design of synthesis prototype filter such that the filter bank pairs distortion function approximates a linear-phase allpass function. Both aliasing and imaging are controlled by introducing sophisticated stopband constraints in both steps. Moreover, we investigate the delay properties of oversampling uniform complex-modulated FIR filter bank pairs in order to achieve the lowest possible filter bank delay. An illustrative design example demonstrates the potential of the design approach.

Robust array interpolation using second-order cone programming

We study Friedlander's (1993) array interpolation technique, whose main shortcoming in multisource scenarios is that it does not provide sufficient robustness against sources arriving outside specified interpolation sectors. In this letter, we develop a new robust interpolation approach by minimizing the interpolation error inside the sectors of interest while setting multiple stopband constraints outside these sectors to prevent performance degradation effects caused by out-of-sector sources. Computationally efficient convex formulations of the robust interpolation matrix design problem using second-order cone programming are derived.

Design methodology of decimation filters for oversampled ADC based on quadratic programming

A design methodology for oversampled analog-to-digital converter decimation filters is presented. The methodology tackles the finite-impulse-response (FIR) filter design problem by formulating a quadratic programming problem that minimizes the integral of the aliased noise subject to the passband and stopband constraints. The approach offers a design whose response is optimized to meet arbitrary quantization noise power spectral density and anti-alias requirements. Because the projected Hessian matrix of the objective function is positive definite, the quadratic function has a unique minimum. The methodology is applied to design filters for different requirements and the performance is compared to conventional approaches.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Design of nonrecursive quadrature mirror filters

A new method of designing nonrecursive quadrature mirror filters with small deviation from the desired overall response is described. By imposing linear constraints at the midpoint of the filter frequency scale, in addition to the normal passband and stopband constraints, a solution that is very close (doubt) optimum is obtained. Satisfactory designs can thus be obtained without resorting to techniques involving the solution of nonlinear constraints. Some results of practical interests are presented.